The New Sudoku Players' Forum

[jco]

Hi !
I am "puzzled" by the following puzzle from Mauricio (source: Sudopedia on "uniqueness clue cover")

Code: Select all

*-----------*
|...|...|...|
|...|...|..2|
|...|..1|...|
|---+---+---|
|..1|.3.|.4.|
|..5|6.7|3..|
|.3.|.2.|..8|
|---+---+---|
|..2|.6.|5..|
|65.|..8|9.4|
|9..|4..|..7|
*-----------*

.................2.....1.....1.3..4...56.73...3..2...8..2.6.5..65...89.49..4....7 ER = 8.4
Following the very short explanation given at the sudopedia site, one can make r1c9=1, solving the puzzle with singles.
From that site:

More dramatically, if a band contains just two clues in the arrangement shown (starred) below, then all of the unclued values are eliminated from two other cells. Note that although it is obvious that -@ in r2c3 implies r2c3=1, this placement is not shown because the elimination of 2 from r2c3 does not require any uniqueness assumption: we are applying the definition strictly.

Code: Select all

+-------------+-------------+-------------+
|   .   .   . |   .   .   . |   .   .  *1 |
|   .   .  -@ |   .   .   . |   .   .  -@ |
|   .   .  *2 |   .   .   . |   .   .   . |
+-------------+-------------+-------------+


These eliminations are available because only a few special types of band (in this case) can be covered by just two clues in any proper, single-solution, puzzle. Knowing the form that these special band types take, by computer searching, allows us to make the eliminations shown.

I may have misunderstood something. Is there (nowadays) a way (proof) to justify that placement using uniqueness but without "computer searching" ? I could not find a thread on this and Wecoc's List of Acronyms points only to Sudopedia.

Many thanks in advance!

[eleven]

If i remember right:
As it says above, all possible solution grids for puzzles with only 2 clues given in a band in different boxes and rows, do have this property (the band alone of course can have many other solutions, but for a unique puzzle solution without that property you would need another given in the band). That was found by exhaustive search.
But i cannot find a reference, when/where that was shown.

[StrmCkr]

reverse bug
by ruud

if i remember correctly covered the early proof and "UCC" yiddish version of "yuck" exhaustively searched unavoidable sets for reduced space to prove it somewhere just as we lost the original server.